Evolutionary homology on coupled dynamical systems with applications to protein flexibility analysis

Area of Science:

• Computational biophysics
• Topology
• Dynamical systems

Background:

• Existing topological persistence methods primarily use spatial filtrations, limiting analysis to global object topology.
• There is a lack of methods to analyze the topology of individual components within a system.
• Component-specific topology is crucial for understanding system properties and function.

Purpose of the Study:

• To develop a novel method, evolutionary homology (EH), for analyzing the topology of individual components within a physical system using temporal filtration.
• To reveal time-dependent topological invariants and topology-function relationships for system components.
• To apply EH to protein flexibility analysis and evaluate its performance.

Main Methods:

• Constructing evolutionary homology (EH) via time evolution-based filtration and topological persistence.
• Coupling dynamical systems or chaotic oscillators representing physical system interactions (e.g., macromolecules) via weighted graph Laplacians.
• Defining simplices, simplicial complexes, algebraic groups, and topological persistence on coupled oscillator trajectories.
• Utilizing Wasserstein metrics for comparative analysis.

Main Results:

• EH generates time-dependent topological invariants, termed evolutionary barcodes, for individual system components.
• The method successfully reveals topology-function relationships.
• In protein flexibility analysis (B-factor prediction), EH significantly outperformed state-of-the-art methods on a benchmark of 364 proteins.

Conclusions:

• Evolutionary homology (EH) provides a powerful new framework for analyzing the topology of individual components in complex systems.
• EH's temporal approach and focus on component-specific topology offer significant advantages over existing methods.
• EH demonstrates high efficacy in predicting protein flexibility, highlighting its potential in computational biophysics and beyond.